Math 242, Spring 2019, Assignment 12
From cartan.math.umb.edu
"When I think of Euclid even now, I have to wipe my sweaty brow."
- - C. M. Bellman
Read:[edit]
- Section 15.8.
- Section 15.9.
Carefully define the following terms, then give one example and one non-example of each:[edit]
- ∂(x,y)∂(u,v) (the Jacobian of the two-dimensional coordinate system (u,v)).
- ∂(x,y,z)∂(u,v,w) (the Jacobian of the three-dimensional coordinate system (u,v,w)).
- ρ,θ, and ϕ (the spherical coordinates of a point in three-dimensional space).
Carefully state the following theorems (you do not need to prove them):[edit]
- Formula for the reduction of double integrals to iterated integrals in an arbitrary two-dimensional coordinate system (i.e. dA=…).
- Formula for the reduction of double integrals to iterated integrals in an arbitrary three-dimensional coordinate system (i.e. dV=…).
- Formulas to convert between rectangular and spherical coordinates.
- Formula for the reduction of double integrals to iterated integrals spherical coordinates (i.e. dV=…).
Solve the following problems:[edit]
- Section 15.8, problems 1, 3, 5, 7, 9, 11, 15, 17, 19, 20, 21, 23, 25, and 41.
- Section 15.9, problems 1, 3, 11, 13, 15, 17, 21(a-b), and 23.